I was checking out my torque wrench. I measure it to be
429mm between the pivots, and made out of a 12.4mm steel rod, that is marked as 150 lb ft when the indicator deflects by 38mm. The indicator is a little short of the outer pivot---the deflection at the outer pivot for 150lbf is around 41mm.I found the formula for deflection: delta = F L^3 / (3 E I)
E is the flexural modulus --- I'll use 180 GPa (Young modulus for steel) F is force applied, L the beam length I is the areal moment of inertia, I = pi/2 r^4
I am going to use the torque instead of force, T=FL, i.e.
delta = T L^2 / (3 E I) = 150 lbf ft (429mm)^2/(3 180 GPa (pi/2) (12.4mm/2)^4)
'units' calculates that as 30mm, a little too short of 41mm measured. Am I making a stupid error somewhere?